Concept explainers
(a)
The probability that the particle will be found in the region.
(a)
Answer to Problem 49P
The probability that the particle will be found in the region is
Explanation of Solution
Given:
The one-dimensional box region is
The particle is in the first excited state.
The given region is
Formula used:
The expression for probability for finding the particle in first excited state is given by,
From integral formula,
Calculation:
Let,
By differentiating both sides,
The limit is
The probability is calculated as,
Solving further as,
Conclusion:
Therefore, the probability that the particle will be found in the region is
(b)
The probability that the particle will be found in the region.
(b)
Answer to Problem 49P
The probability that the particle will be found in the region is
Explanation of Solution
Given:
The given region is
Formula used:
The expression for probability for finding the particle in first excited state is given by,
From integral formula,
Calculation:
Let,
By differentiating both sides,
The limit is
The probability is calculated as,
Solving further as,
Conclusion:
Therefore, the probability that the particle will be found in the region is
(c)
The probability that the particle will be found in the region.
(c)
Answer to Problem 49P
The probability that the particle will be found in the region is
Explanation of Solution
Given:
The given region is
Formula used:
The expression for probability for finding the particle in ground state is given by,
From integral formula,
Calculation:
Let,
By differentiating both sides,
The limit is
The probability is calculated as,
Solving further as,
Conclusion:
Therefore, the probability that the particle will be found in the region is
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Chapter 34 Solutions
Physics for Scientists and Engineers, Vol. 3
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